Topology invisible to eigenvalues in obstructed atomic insulators

Abstract

We consider the extent to which symmetry eigenvalues reveal the topological character of bands. Specifically, we compare distinct atomic limit phases (band representations) that share the same irreducible representations (irreps) at all points in the Brillouin zone and, therefore, appear equivalent in a classification based on eigenvalues. We derive examples where such "irrep-equivalent" phases can be distinguished by a quantized Berry phase or generalization thereof. These examples constitute a generalization of the Su-Schrieffer-Heeger chain: neither phase is topological, in the sense that localized Wannier functions exist, yet there is a topological obstruction between them. We refer to two phases as "Berry obstructed atomic limits" if they have the same irreps, but differ by Berry phases. This is a distinct notion from eigenvalue obstructed atomic limits, which differ in their symmetry irreps at some point in the Brillouin zone. We compute exhaustive lists of elementary band representations that are irrep-equivalent, in all space groups, with and without time-reversal symmetry and spin-orbit coupling, and use group theory to derive a set of necessary conditions for irrep-equivalence. Finally, we conjecture, and in some cases prove, that irrep-equivalent elementary band representations that are not equivalent can be distinguished by a topological invariant.

arXiv comment18 pages, plus tables and Supplementary Material

References in corpus (78)

• Topological Insulators with Inversion Symmetry
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Topological Crystalline Insulators in the SnTe Material Class
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• The (High Quality) Topological Materials In The World
• Experimental realization of a topological crystalline insulator in SnTe
• Reflection symmetric second-order topological insulators and superconductors
• Catalogue of Topological Electronic Materials
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Higher-Order Topology in Bismuth
• Topological crystalline insulator states in Pb(1-x)Sn(x)Se
• Odd-Parity Topological Superconductors: Theory and Application to Cu${}_x$Bi${}_2$Se${}_3$
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• A topological crystalline insulator (TCI) phase via topological phase transition and crystalline mirror symmetry
• Antiferromagnetic topological insulators
• The space group classification of topological band insulators
• Topological classification of crystalline insulators through band structure combinatorics
• Inversion Symmetric Topological Insulators
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Topology of crystalline insulators and superconductors
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Wannier representation of Z_2 topological insulators
• Hourglass Fermions
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Fragile Topology and Wannier Obstructions
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Quantitative mappings between symmetry and topology in solids
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Double crystallographic groups and their representations on the Bilbao Crystallographic Server
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Magnetic Topological Quantum Chemistry
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Topological classification with additional symmetries from Clifford algebras
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Topological odd-parity superconductors
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs
• Wannier Center Sheets in Topological Insulators
• Topological Materials Discovery from Crystal Symmetry
• Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations
• Topological non-symmorphic crystalline insulators
• Topological Crystalline Insulators and Dirac Octets in Anti-perovskites
• Experimental Discovery of the First Nonsymmorphic Topological Insulator KHgSb
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• Rotation Anomaly and Topological Crystalline Insulators
• Topological Classification of Crystalline Insulators with Point Group Symmetry
• Topology of Disconnected Elementary Band Representations
• Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
• The chiral anomaly factory: Creating Weyl fermions with a magnetic field
• Topological Insulators from Group Cohomology
• Graph Theory Data for Topological Quantum Chemistry
• Band Representations and Topological Quantum Chemistry
• Topological Insulators with Commensurate Antiferromagnetism
• New class of topological superconductors protected by magnetic group symmetries
• Band Connectivity for Topological Quantum Chemistry: Band Structures As A Graph Theory Problem
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Multifold nodal points in magnetic materials
• Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry
• Topological Bloch oscillations
• A systematic study of stacked square nets: from Dirac fermions to material realizations
• Symmetry indicators for topological superconductors
• Multicellularity of delicate topological insulators
• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• Higher-order topological insulators in antiperovskites
• Application of the induction procedure and the Smith Decomposition in the calculation and topological classification of electronic band structures in the 230 space groups
• Bott periodicity for the topological classification of gapped states of matter with reflection symmetry
• Topological Crystalline Phases in a Disordered Inversion-Symmetric Chain
• No-go theorem for topological insulators and sure-fire recipe for Chern insulators
• The Z_2 network model for the quantum spin Hall effect: two-dimensional Dirac fermions, topological quantum numbers, and corner multifractality
• Revisiting (higher order and crystalline) topology in old models of lead telluride

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• All Topological Bands of All Nonmagnetic Stoichiometric Materials
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• General theory of Josephson Diodes
• Amorphous topological matter: theory and experiment
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• Obstructed insulators and flat bands in topological phase-change materials
• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
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• Orbital shift-induced boundary obstructed topological materials with a large energy gap
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
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